Heretofore, a horizontal continuous casting installation of the aforesaid construction has been constructed such that the tundish nozzle and the mold are intimately connected to each other to keep a body of molten metal from leaking between the tundish nozzle formed of refractory material and the mold cooled with water. Because of this, the cooled molten metal has tended to form a shell of solidified molten metal on the outer side of the body of molten metal in the vicinity of the tundish nozzle adjacent the water-cooled mold as the molten metal begins to solidify at its outer side and become adhered to the tundish nozzle. Also, the molten metal has tended to invade the refractory material through the pores and become solidified therein, to thereby increase bond strength between the shell and the tundish nozzle. When this is the case, the shell formed by solidification of the molten metal undergoes rupture when the strand is withdrawn to thereby give rise to what is generally referred to as a break-out.